Recession cone

Mathematical definition

Properties

• If is a nonempty set then.
• If is a nonempty convex set then is a convex cone.
• If is a nonempty closed convex subset of a finite-dimensional Hausdorff space, then if and only if is bounded.
• If is a nonempty set then where the sum denotes Minkowski addition.

  Relation to asymptotic cone

Sum of closed sets

• Dieudonné's theorem: Let nonempty closed convex sets a locally convex space, if either or is locally compact and is a linear subspace, then is closed.
• Let nonempty closed convex sets such that for any then, then is closed.